Hirsch Conjecture 2

Here is more information about the counterexample to the Hirsch conjecture:

“my proof has two parts: (1) there is a 5-polytope with 48 facets, with the following properties: it has two vertices $u$ and $v$ contained in all the facets (each in 24 of them) and no path of length five joins $u$ to $v$. (2) Then there is what I call the “generalized $d$-step theorem” saying that from this, using certain wedges and perturbations, you can get a 43-dimensional polytope with 86 facets and without the Hirsch property. Part (1) is totally explicit and has been verified with computer software (polymake). Part (2) is not explicit.”